Question

Q.12.The length of a rectangular
plot of land is twice its breadth.If
the perimeter of the plot be 180
metres,then its area is -
O 1600 sq.m
0 1700 sq.m
O 1800 sq.m.
SI
O
1900 sq.m.​

Answer 1

Answer :

★ Option 1800 sq.m is correct ✔

Given :

• The length of a rectangular
• plot of land is twice its breadth.
• The perimeter of the plot be 180
• metres.

Find :

• The area of the rectangle

$\large{\mathfrak{\underline{Solution :-}}}$

Here, we have the length of the rectangular plot is twice its breadth and also the perimeter

So,

Let the breadth be x

And Let the length be 2x

★ Formula for perimeter of Rectangle :

$\large{\boxed{\sf{Perimeter\;of\;Rectangle = 2 ( length + breadth ) }}}$

» Put values in formula

= ${\sf{Perimeter\;of\;Rectangle = 2 ( length + breadth ) }}$

= ${\sf{180 = 2 ( 2x + x ) }}$

= ${\sf{180 = 2 × 3x }}$

= ${\sf{180 = 6x }}$

= ${\sf{\dfrac{180}{6} = x }}$

= ${\sf{ 30 = x }}$

Thus,

➡ Length = 2x = 2 × 30 = 60 m

➡ Breadth = x = 30 m

Now,

As asked in the question , let us find the area of the rectangle.

★ Formula for area of Rectangle

$\large{\boxed{\sf{Area\;of\;Rectangle = length × breadth }}}$

» Putting values in formula

= ${\sf{Area\;of\;Rectangle = length × breadth }}$

= ${\sf{Area\;of\;Rectangle = 60 × 30 }}$

= ${\sf{Area\;of\;Rectangle = 1800 }}$

•°• The area of the rectangle is 1800 m² respectively .

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